Question

The radii of two concentric circles are 17 cm and 10 cm A line ABCD cuts a circle at A,D and other at B and C . If BC=12 cm then the length of AB is

• A. 8 cm
• B. 9 cm
• C. 7 cm
• D. 6 cm

Answer 1

The correct option is B 9 cm

The figure is shown in image

Now apply Pythagoras theorem in $\Delta CMO$

$O{C}^2=C{M}^2+O{M}^2$

${10}^2=6^2+O{M}^2$

$OM=8$c.m.

Now apply Pythagoras theorem in $\Delta MOD$

$O{D}^2=D{M}^2+O{M}^2$

${17}^2=D{M}^2+8^2$

$DM=15$c.m.$=AM$

Hence $AM=AB+BM$

$AB=15-6$

$AB=9$c.m.